





'''simple docstring'''




def 			_lowerCAmelCase     (    __snake_case    :					Optional[int]     )	->	Optional[int]:
     __A		:					List[str]						=			0
     __A		:					Optional[int]						=			len(__snake_case     )

     for i in range(n - 1     ):
          for j in range(i + 1					,				__snake_case     ):
               if arr[i] > arr[j]:
                    num_inversions += 1

     return num_inversions






def 			_lowerCAmelCase     (    __snake_case    :					Tuple     )	->	Optional[Any]:
     if len(__snake_case     ) <= 1:
          return arr, 0
     __A		:					List[Any]						=			len(__snake_case     ) // 2
     __A		:					int						=			arr[0:mid]
     __A		:					List[Any]						=			arr[mid:]

     __A					,__A		:					Optional[Any]						=			count_inversions_recursive(__snake_case     )
     __A					,__A		:					Any						=			count_inversions_recursive(__snake_case     )
     __A					,__A		:					str						=			_count_cross_inversions(__snake_case					,				__snake_case     )

     __A		:					int						=			inversion_p + inversions_q + cross_inversions
     return c, num_inversions






def 			_lowerCAmelCase     (    __snake_case    :					Union[str, Any]					,				__snake_case    :					List[str]     )	->	Tuple:
     __A		:					List[str]						=			[]
     __A		:					Optional[int]						=			0
     while i < len(__snake_case     ) and j < len(__snake_case     ):
          if p[i] > q[j]:
               # if P[1] > Q[j], then P[k] > Q[k] for all  i < k <= len(P)
               # These are all inversions. The claim emerges from the
               # property that P is sorted.
               num_inversion += len(__snake_case     ) - i
               r.append(q[j]     )
               j += 1
          else:
               r.append(p[i]     )
               i += 1

     if i < len(__snake_case     ):
          r.extend(p[i:]     )
     else:
          r.extend(q[j:]     )

     return r, num_inversion






def 			_lowerCAmelCase     (    )	->	Any:
     __A		:					Optional[Any]						=			[10, 2, 1, 5, 5, 2, 11]

     # this arr has 8 inversions:
     # (10, 2), (10, 1), (10, 5), (10, 5), (10, 2), (2, 1), (5, 2), (5, 2)

     __A		:					Tuple						=			count_inversions_bf(__snake_case     )
     __A					,__A		:					Optional[Any]						=			count_inversions_recursive(__snake_case     )

     assert num_inversions_bf == num_inversions_recursive == 8

     print('number of inversions = '					,				__snake_case     )

     # testing an array with zero inversion (a sorted arr_1)

     arr_a.sort()
     __A		:					str						=			count_inversions_bf(__snake_case     )
     __A					,__A		:					Any						=			count_inversions_recursive(__snake_case     )

     assert num_inversions_bf == num_inversions_recursive == 0
     print('number of inversions = '					,				__snake_case     )

     # an empty list should also have zero inversions
     __A		:					Union[str, Any]						=			[]
     __A		:					List[Any]						=			count_inversions_bf(__snake_case     )
     __A					,__A		:					List[Any]						=			count_inversions_recursive(__snake_case     )

     assert num_inversions_bf == num_inversions_recursive == 0
     print('number of inversions = '					,				__snake_case     )


if __name__ == "__main__":
  main()

from ..utils import is_flax_available, is_torch_available


if is_torch_available():
							from .autoencoder_kl import AutoencoderKL
							from .controlnet import ControlNetModel
							from .dual_transformer_ad import DualTransformeraDModel
							from .modeling_utils import ModelMixin
							from .prior_transformer import PriorTransformer
							from .ta_film_transformer import TaFilmDecoder
							from .transformer_ad import TransformeraDModel
							from .unet_ad import UNetaDModel
							from .unet_ad import UNetaDModel
							from .unet_ad_condition import UNetaDConditionModel
							from .unet_ad_condition import UNetaDConditionModel
							from .vq_model import VQModel

if is_flax_available():
							from .controlnet_flax import FlaxControlNetModel
							from .unet_ad_condition_flax import FlaxUNetaDConditionModel
							from .vae_flax import FlaxAutoencoderKL






